This is a textbook on ordinary differential equations in their applied aspects and it caters to students with a physico-mathematical profile, as well as those in informatics and cybernetics. This book also caters to educators who study the pedagogy of teaching mathematics, especially on differential equations.Containing over 400 solved examples and problems, its main objective is to promote a deep understanding on the theory, develop concrete mathematical thinking of students, nurture the skills in finding solutions to the problems, and understand their physical essence.This book completely covers all parts of the course on ordinary differential equations taught at universities: first-order differential equations, high-order differential equations, systems of differential equations, stability theory and so on.